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Open AccessJournal ArticleDOI

A family of embedded Runge-Kutta formulae

J. R. Dormand, +1 more
- 01 Mar 1980 - 
- Vol. 6, Iss: 1, pp 19-26
TLDR
In this article, a family of embedded Runge-Kutta formulae RK5 (4) are derived from these and a small principal truncation term in the fifth order and extended regions of absolute stability.
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This article is published in Journal of Computational and Applied Mathematics.The article was published on 1980-03-01 and is currently open access. It has received 3106 citations till now.

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Bose-Einstein condensates with balanced gain and loss beyond mean-field theory

Dennis Dast, +4 more
- 01 Nov 2016 - 
TL;DR: In this article, the authors study the many-particle dynamics of a two-mode condensate with balanced gain and loss described by a master equation in Lindblad form whose purity periodically drops to small values but then is nearly completely restored.
DOI

Zero-dimensional models for plasma chemistry

Waad Wouter Graef
TL;DR: In this paper, two different collisional radiative models for examining the chemistry in a plasmas are studied: collisional radiative models (CRM) and global plasma models (GPM).
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A generic mechanism for finite-size coherent particle structures

Francesco Romanò, +3 more
- 01 Feb 2019 - 
TL;DR: In the absence of inertia, particles can also cluster massively in a steady flow, solely owing to their size when they are repelled from a boundary by lubrication and lift forces.
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Modeling the Chemical Impact and the Optical Emissions Produced by Lightning‐Induced Electromagnetic Fields in the Upper Atmosphere: The case of Halos and Elves Triggered by Different Lightning Discharges

F. J. Pérez-Invernón, +2 more
- 27 Jul 2018 - 
TL;DR: In this article, the simulation data and plot codes presented here are available from figshare repository at https://figshare.com/s/f1c9f6c7 bc728d6669dd.
Journal ArticleDOI

Analysis of friction-induced vibration in a propeller–shaft system with consideration of bearing–shaft friction

Zhenguo Zhang, +3 more
TL;DR: In this paper, the friction-induced vibration of a continuous propeller-shaft system excited by nonlinear friction due to contact between a water-lubricated bearing and a shaft was investigated.
References
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Book

Computational Methods in Ordinary Differential Equations

John Denholm Lambert
Journal ArticleDOI

Comparing Numerical Methods for Ordinary Differential Equations

T. E. Hull, +3 more
- 01 Dec 1972 - 
TL;DR: According to criteria involving the number of function evaluations, overhead cost, and reliability, the best general-purpose method, if function evaluations are not very costly, is one due to Bulirsch and Stoer, however, when function evaluated methods are relatively expensive, variable-order methods based on Adams formulas are best.

Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems

E. Fehlberg
Journal ArticleDOI

Coefficients for the study of Runge-Kutta integration processes

John C. Butcher
- 01 May 1963 - 
TL;DR: In this paper, a set of η first order simultaneous differential equations in the dependent variables y 1, y 2, y 3, y 4, y 5, y 6 and the independent variable x is considered.

Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control

E. Fehlberg
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.